cpucpu-architecturememory-bandwidthroofline

Question about bandwidth ceilings in roofline models

I don't quite understand the bandwidth factor in roofline models described in Wikipedia (like the pic and its caption shown below):

  1. why the intersection between the β x I and axises could be changed? Why could there be performance while operation intensity is zero?
  2. When changing bandwidth ceilings, why the slope of the β x I does not change?

enter image description here

An example of a Roofline model with added bandwidth ceilings. In this model, the two additional ceilings represent the absence of software prefetching and NUMA organization of memory. -- Wikipedia

Solution

  • The axes in this graph are logarithmic. So the zero intensity case is not actually on the graph. Also, because of that logarithmic scale, any factor degradation, for instance from lack of prefetching, is a constant displacement.